Julian Day Conversion (Meeus formula):

A = floor(Y / 100)

B = 2 - A + floor(A / 4)

JD = floor(365.25 × (Y + 4716)) + floor(30.6001 × (M + 1)) + D + H/24 + B - 1524.5

Then: T = (JD - 2451545.0) / 36525.0 → centuries from J2000.0

Our Sun algorithm (Meeus Ch. 25):

L0 = 280.46646 + 36000.76983 × T // mean longitude

M = 357.52911 + 35999.05029 × T // mean anomaly

C = 1.9146 × sin(M) + 0.02 × sin(2M) // equation of center

Sun_true = L0 + C

Sun_apparent = Sun_true - 0.00569 - 0.00478 × sin(Ω) // nutation

Moon longitude — 60-term algorithm:

L' = 218.316 + 481267.881 × T // Moon mean longitude

D = 297.850 + 445267.111 × T // mean elongation

M = 357.529 + 35999.050 × T // Sun mean anomaly

M' = 134.963 + 477198.868 × T // Moon mean anomaly

F = 93.272 + 483202.018 × T // argument of latitude

Σl = Σ [coeff × sin(D×d + M×m + M'×m' + F×f)] × E^|m|

Moon_long = L' + Σl/1000000 + A1 + A2 + A3 corrections

शीर्ष 4 पद: 6.289° sin(M'), 1.274° sin(2D-M'), 0.658° sin(2D), 0.214° sin(2M')

E = उत्केन्द्रता सुधार: 1 - 0.002516×T

Lahiri Ayanamsha polynomial:

Ayanamsha = 23.85306° + 1.39722° × T + 0.00018° × T²

where T = centuries from J2000.0

Sidereal_longitude = Tropical_longitude - Ayanamsha

2026 के लिए: अयनांश ≈ 24.22° → 50° उष्णकटिबन्धीय पर ग्रह ~25.78° नाक्षत्रिक पर है

Binary Search Algorithm:

jd_low = sunrise_JD

jd_high = sunrise_JD + 1.5 // 36 hours window

while (jd_high - jd_low > 0.0001): // ~8.6 sec precision

mid = (jd_low + jd_high) / 2

if tithi(mid) == current_tithi:

jd_low = mid // transition is after mid

else:

jd_high = mid // transition is before mid

Converges in ~20 iterations → ~40 function evaluations per element

Sunrise calculation:

decl = asin(sin(23.44°) × sin(Sun_long))

cos(H) = (sin(-0.833°) - sin(lat) × sin(decl)) / (cos(lat) × cos(decl))

sunrise_UT = 12h - H/15 - longitude/15

-0.833° वायुमण्डलीय अपवर्तन + सौर तश्तरी अर्धव्यास का हिसाब